This invention relates to frequency offset estimation and correction and more particularly to frequency offset correction by least squares training sequence processing.
Adaptive array antennas are widely proposed for cellular radio base stations, see the technical article xe2x80x9cSmart Antennas for Wireless Systemsxe2x80x9d, Jack H. Winters, IEEE Personal Communications, vol. 5, no. 1, February, 1998. An adaptive array antenna is an array of two or more antenna elements and specialized signal processing to combine the antenna outputs into a single array output. These antennas are called adaptive because their directional sensitivities change in response to the signal environment. Adaptive antennas are commonly controlled by a least squares algorithm. This invention uses the variables normally computed by the least squares algorithm in controlling an adaptive antenna to estimate and correct frequency offsets in the desired received signals.
Adaptive antennas have several advantages over conventional antennas. First, adaptive antennas combine the element signals to provide optimized signal to interference plus noise ratio (S/(N+I)) in the array output. In so doing, it maximizes the desired signal while minimizing or nulling the undesired signals. Secondly, because the antenna adapts to the signal environment, changes are xe2x80x9ctrackedxe2x80x9d as they occur in the environment. In particular, the cellular environment is characterized by fading and multipath transmission due to motion of the mobile phones. The signals at the elements of the array fade in a random manner. An adaptive antenna can track the fading, continually adjusting how the elements are combined to form the output, so that the fading is minimized at the array output for the desired signal.
To operate properly, the adaptive antenna recognizes desired signals from undesired signals. In the IS-136 digital cellular system, least squares processing in conjunction with a xe2x80x9ctrainingxe2x80x9d or reference sequence is commonly proposed to control an adaptive antenna. Each mobile phone transmits an assigned sequence of 14 symbols (the reference sequence) periodically. The reference data sequence received by an antenna is compared with an internal reference sequence stored in the base station. Received signals that match the reference sequence are maximized, while all others are minimized. The reference sequence was originally included in the IS-136 standard for the control of adaptive equalizers. However, the reference sequence may also be used for the control of adaptive antennas. The reference sequence is used in a batch least squares computation to compute optimal weighting coefficients for combining the element signals into a single output. See, for example, Solving Lease Squares Problems, by Charles L. Lawson and Richard J. Hanson, Prentice-Hall, Inc. Englewood Cliffs, N.J., 1974, and xe2x80x9cSolving Linear Least Squares Problems by Gram Schmidt Orthogonalizationxe2x80x9d, Ake Bjork, Nordisk Tidskr. Informations-Behandling (BIT), vol. 7, 1967, pp. 1-21, for prior art batch least squares descriptions. One set of coefficients is computed for the complete reference sequence (i.e. the batch of 14 symbols), hence the name batch least squares. In performing the computation of optimal coefficients, many least squares algorithms compute error samples as intermediate variables in the computation. Error samples are the difference between the received output reference samples and the internal base station reference samples. The present invention uses these error samples to compute an estimate of the carrier frequency offset of the received output signal.
The mobile phone transmits voice data both before and after the reference sequence. Unlike the reference data sequence, the voice data is not known apriori, and different processing must be used. These data are processed by recursive least squares computations as described in the technical article xe2x80x9cA Recursive Modified Gram-Schmidt Algorithm for Least Squares Estimationxe2x80x9d, Fuyun Ling, Dimitris Manolakis, and John G. Proakis, IEEE Trans. on Acoustics, Speech, and Signal Processing, vol. ASSP-34, No. 4, August, 1986, pp. 829-836. In the recursive least squares computations, the optimal combining coefficients are updated recursively on a symbol by symbol basis. A reference symbol is still needed for each received data symbol. Here, however, the reference symbol is derived from the current data symbol using coefficients computed for the previous data symbol. This is called a data derived reference. The initial coefficients obtained by batch processing of the training sequence are used to initialize the recursions.
The recursive least square processing used to control the adaptive antenna is sensitive to carrier frequency errors. A frequency error occurs when the carrier frequency transmitted from the mobile phone is incorrect. This is usually due to the poor quality frequency sources used in the mobile to minimize cost (up to 200 Hz. error is permitted in the IS-136 standard. EIA Interim Standard IS-136.2, Electronic Industries Alliance, Arlington, Va.). The IS-136 system uses xcfx80/4 offset DQPSK (differential quadrature phase shift keying), in which each symbol is coded into discrete phase states. A DQPSK frequency error causes the received symbols to have a progressive (i.e. increasing with each symbol) phase rotation in addition to symbol phases. The maximum permitted frequency offset of 200 Hz. causes a phase shift of approximately 3xc2x0 per symbol. This does not cause major problems over the 14-symbol batch least squares processing of the training sequence data. However, over the typical 134 voice data symbols following the training sequence, the phase progression is sufficient to cause a failure of the recursive least squares processing.
There are several existing techniques for tracking and removing the carrier frequency error as described in Data Communications Principles, by Richard D. Gitlin, Jeremiah F. Hayes, and Stephen B. Weinstein, Plenum Press, New York, 1992, pp. 433 ff. Most of these are based on phased lock loop (PLL) concepts. These include the squaring loop, the Costas loop, and the data-directed PLL. Unfortunately, all these techniques are susceptible to interference. Thus, using one of these techniques to correct the frequency offset before the adaptive processing is not beneficial. The frequency correction technique will fail with the interference, thus causing the failure of the adaptive processing. Also, the use of a separate correction technique is undesirable because of the added computational cost and circuit complexity incurred.
Therefore in accordance with this invention the frequency errors are measured and corrected within the adaptive processing itself, thereby providing the frequency correction with significant immunity to interference without incurring excessive additional computations or hardware.
In accordance with the present invention, there is provided a method for correcting the frequency offset of a dataset by utilization of errors computed by least squares training sequence processing. These errors may be computed in the normal course of adaptive antenna or adaptive equalizer processing and are available in such systems without additional computation. The errors are utilized to estimate the frequency offset and the estimated offset is then used as a correction factor to correct the frequency offset of the dataset.
Further in accordance with the present invention, there is provided a method for correcting the frequency offset of received signals of a dataset by computing a least squares weight solution for a batch of data samples in a training sequence to obtain the least square error for each data sample. Each error sample is rotated by multiplication by the conjugate of a reference sample comprising a sample from the training sequence and then each rotated error sample is numbered in the order received. The slope of a line having a best fit to the set of imaginary parts of the rotated error samples is computed as a function of the number of each rotated error sample to obtain a value for a frequency offset estimate. Each data sample of the dataset is multiplied by an expression that includes the estimated frequency offset to obtain frequency offset corrected data samples. The frequency offset corrected data samples are recursively processed by a least square computation utilizing the frequency offset corrected sample to obtain corrected received signals for further receiver processing.
Further in accordance with the present invention, there is provided a method for correcting the frequency offset of received signals of a dataset by computing a plurality of values of estimated frequency offset and filtering the plurality of values to obtain filtered value for an enhanced frequency offset correction value.